One of the significant advantages of legged robots over other types of mobile robots, such as wheeled robots, is that they possess the capability of traversing uneven terrains and functioning in harsh environments [1]}, [2]}. Stabilizing bipedal robots' gait while operating in an unknown environment, specifically when they walk on an uneven surface, is crucial for achieving robust bipedal mobilization. Besides the unknown profile of the ground, uncertainty, clearance, and errors in actuators, links and joints are other sources of instability that can mitigate the robot’s body fluctuations even when walking on perfectly flat surfaces. Another major challenge regarding the smooth walking of position-controlled robots is the disturbance exerted on the robot body by contact force impacts from each sole at the beginning of the support phase [3]}. This problem becomes more significant when the walking pace of the robot increases, so minimizing the effects of ground reaction forces impact that occurs in the swing sole contact change is essential for reaching higher walking speeds. Humanoids' reliable, human-level walking ability depends on maintaining a smooth and continuous contact change between the robot's soles and the ground with minimal contact impact [4]}. The most utilized and venerated criteria for checking the stability of a bipedal robot is Zero Moment Point (ZMP); this is a necessary condition. Dynamic stability of walking is not within the scope of this work; however, it is worth mentioning that the ZMP stability criterion is a necessary but not sufficient condition for contact wrench stability [5]}. As a result of that, when dealing with position-controlled humanoid robots, the individual contact force distributed at each sole should be studied to address the sole impact disturbance problems [6]}. Admittance controllers are used to control the forces, reduced model[7]}, [8]}, [9]} or torques of the position-controlled humanoid robots in a effector (wrist or ankle) [10]}, [11]}.
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